The water heater I'm referring to does have the insulation underneath the thin metal sleeve. I'm wondering if puting additional insulation around the
unit will help, or if the additional insulation is insignificant?

The water heater I'm referring to does have the insulation underneath the thin metal sleeve. I'm wondering if puting additional insulation around the
unit will help, or if the additional insulation is insignificant?

Molo

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Put your hand on the water heater shell. Does it feel significantly warm? Better yet, measure the temperature of the metal shell. If it is more than a few degrees warmer than the surroundings, add insulation. Do the test early in the morning when the space around the heater is at it's coolest.

Read all the lables on the outside of the heater. Some manufacturers specifically say not to use a thermal blanket on the outside of the heater. Heat loss is a function of the temperature difference between the ambient air and the water heater's temperature. So the cooler room is going to cost some additional electrical consumption, but probably not a great deal.